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The last few years have seen the development of a promising theoreticalframework for statistics of the cosmic large-scale structure -- the theory oflarge deviations (LDT) for modelling weak-lensing one-point statistics in themildly non-linear regime. The goal of this series of papers is to make the leapand lay out the steps to perform an actual data analysis with this theoreticaltool. Building upon the LDT framework, in this work (Paper I) we demonstratehow to accurately model the Probability Distribution Function (PDF) of areconstructed Kaiser-Squires convergence field under a realistic mask, that ofthe third data release of the Dark Energy Survey (DES). We also present howweak lensing systematics and higher-order lensing corrections due to intrinsicalignments, shear biases, photo-$z$ errors and baryonic feedback can beincorporated in the modelling of the reconstructed convergence PDF. In anupcoming work (Paper II) we will then demonstrate the robustness of ourmodelling through simulated likelihood analyses, the final step required beforeapplying our method to actual data.

Making the leap I: Modelling the reconstructed lensing convergence PDF from cosmic shear with survey masks and systematics